HYDRODYNAMICS OF SUPERFLUID HELIUM WITH SUPERFLUID ENTROPY

Developing air-water bubble flows in a vertical pipe were calculated using the combination of a multi-fluid model and an interfacial area concentration (IAC) transport equation. Calculations were conducted by using (a) a standard two-fluid model, (b) a two-fluid model and a one-group IAC equation, (c) a two-fluid model and a two-group IAC equation and (d) a three-fluid model and a two-group IAC equation. As a result of comparisons between measured and calculated void fractions, we confirmed that (1) the use of IAC equations brings about the reconstruction or reconsideration of interfacial drag models, (2) the two-group IAC equation requires initial values for a large bubble group even for the condition of no large bubbles, (3) the combination of the two-group IAC equation and two-fluid model cannot give good predictions for flows consisting of large and small bubbles, and (4) a multi-fluid model and a reconstructed drag force model are indispensable to obtain good predictions for bubbly to slug flow transition.

Accurate prediction of pressure drop of the heavy oil-water ring flow in pipeline is of great significance for establishing an optimal drag reduction model and ensuring safe production. The effects of different factors on the flow pattern and pressure drop of heavy oil-water annular two-phase flow were systematically analyzed, and a standard two-fluid pressure drop prediction model for annular flow was established. By modifying the shear stress equation of oil-water interface and introducing the wave-flow theory to modify the shear stress equation of water wall, a pressure drop prediction model for the generalized concentric water ring was obtained to calculate the periodic fluctuations of oil phase. Furthermore, by introducing the comprehensive Reynolds number expression of eccentric water ring, the pressure drop prediction model for the generalized eccentric water ring was obtained to calculate the periodic fluctuations of oil phase. The results show that the pressure drop prediction accuracy of the concentric water ring for ultra-heavy oil is improved by 80% by using the modified pressure drop prediction model. The comprehensive Reynolds number expression of eccentric water ring can effectively reflect the influence of eccentric effect on shear stress of water wall and the calculation error is less than 20% by predicting the pressure drop of the generalized eccentric water ring with different density differences.

End-to-end modelling of He II flow systems

Simulation of 3D freely bubbling gas–solid fluidized beds using various drag models: TFM approach

Estimation of the spatial discretization error in numerical simulations of bubbly flows

The two-fluid model is widely used to describe two-phase flows in complex systems such as nuclear reactors. Although the two-phase flow was successfully simulated, the standard two-fluid model suffers from an ill-posed nature. There are several remedies for the ill-posedness of the one-dimensional (1D) two-fluid model; among those, artificial viscosity is the focus of this study. Some previous works added artificial diffusion terms to both mass and momentum equations to render the two-fluid model well-posed and demonstrated that this method provided a numerically converging model. However, they did not consider mass conservation, which is crucial for analyzing a closed reactor system. In fact, the total mass is not conserved in the previous models. This study improves the artificial viscosity model such that the 1D incompressible two-fluid model is well-posed, and the total mass is conserved. The water faucet and Kelvin-Helmholtz instability flows were simulated to test the effect of the proposed artificial viscosity model. The results indicate that the proposed artificial viscosity model effectively remedies the ill-posedness of the two-fluid model while maintaining a negligible total mass error.

This article examines a 1D incompressible two-fluid model including artificial tensor diffusion. The aim is to obtain a formulation that provides convergent numerical solutions for all flow conditions within the stratified and the stratified wavy flow regime. With appropriate simplifications, the two-fluid model reduces to one momentum balance, one mass conservation and two algebraic equations. It has previously been established that a formulation that is well posed in possessing exclusively real characteristics can be obtained by including an axial diffusion term in the momentum balance. In this article, however, we demonstrate that this is not sufficient to obtain a system suitable for numerical simulations. Although the unbounded growth rates of the standard two-fluid model are eliminated, linear stability theory predicts that infinitesimal wavelengths still experience finite growth. This entails that grid refinement always will result in new unstable wavelengths being resolved. On the other hand, if artificial axial diffusion is added to both the mass and the momentum equations as suggested here, a cut-off wavelength is established below which all wavelengths are stable. Thus, a numerically converging model is formed, which retains the long-wavelength properties of the standard two-fluid model. The conclusions of the mathematical analysis are substantiated by numerical simulations of ID gravity waves.

In this article nucleosynthesis will be investigated in a class of cosmological models in which two separate interacting fluids act as the source of the gravitational field, a comoving radiative perfect fluid modelling the cosmic-microwave background and a second fluid modelling the observed material content of the Universe. The two-fluid models under consideration are found to predict primordial element abundances very similar to those predicted in the standard model and consequently in general accord with observed abundances. Since the evolution of the baryon density in the models is different to that in the standard model the inferred limits on the present baryon density will also be different. In the models under investigation the range of values for the present baryon density consistent with observed light element abundances is found to be far wider, and in particular the allowed upper limit on the present baryon density is found to be greater, than in the standard case.

We consider a simple experimental setup, based on a harmonic confinement, where a Bose-Einstein condensate and a thermal cloud of weakly interacting alkali-metal atoms are trapped in two different vessels connected by a narrow channel. Using the classical field approximation, we theoretically investigate the analog of the celebrated superfluid-helium fountain effect. We show that this thermomechanical effect might indeed be observed in this system. By analyzing the dynamics of the system, we are able to identify the superfluid and normal components of the flow as well as to distinguish the condensate fraction from the superfluid component. We show that the superfluid component can easily flow from the colder vessel to the hotter one while the normal component is practically blocked in the latter. In the long-time limit, the superfluid component exhibits periodic oscillations reminiscent of the ac Josephson effect obtained in superfluid weak-link experiments.

The Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model is widely used to numerically study quantum turbulence in superfluid helium. Based on the two-fluid model of Tisza and Landau, the HVBK model describes the normal (viscous) and superfluid (inviscid) components of the flow using two Navier–Stokes type of equations, coupled through a mutual friction force term. We derive transport equations for the third-order moments for each component of velocity involving the fourth-order moments, which are classical probes for internal intermittency at any scale, and revealing the probability of rare and strong fluctuations. Budget equations are assessed through direct numerical simulations of the HVBK flow. We simulate a forced homogeneous isotropic turbulent flow with Reynolds number of the normal fluid (based on Taylor's microscale) close to 100. Values from 0.1 to 10 are considered for the ratio between the normal and superfluid densities. For these flows, an inertial range is not discernible and the restricted scaling range approach is used to take into account the finite Reynolds number (FRN) effect. We analyse the importance of each term in budget equations and emphasize their role in energy exchange between normal and superfluid components. Some interesting features are observed: (i) transport and pressure-related terms are dominant, similarly to single-fluid turbulence; and (ii) the mathematical signature of the FRN effect is weak despite the low value of the Reynolds number. The flatness of the velocity derivatives is finally studied through the transport equations and their limit for very small scales, and it is shown to gradually increase for lower and lower temperatures, for both normal fluid and superfluid. This similarity highlights the strong locking of the two fluids. The flatness factors are also found in reasonable agreement with classical turbulence.

A one-fluid model of superfluids

The one dimensional two-fluid model is widely acknowledged as the most detailed and accurate macroscopic formulation model of the thermo-fluid dynamics in nuclear reactor safety analysis. Currently the prevailing one dimensional thermal hydraulics codes are first order accurate. The benefit of first order schemes is numerical viscosity, which serves as a regularization mechanism for many otherwise ill-posed two-fluid models. However, excessive diffusion in regions of large gradients leads to poor resolution of phenomena related to void wave propagation. In this work, a second order numerical method is developed for a standard two-fluid model code by applying a second order temporal scheme and a shock capturing scheme using a flux limiter formulation for the convection of void fraction and velocity. The classic water faucet problem is taken as the benchmark.Copyright © 2012 by ASME

view Abstract Citations (84) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Propagation of adiabatic cosmological perturbations through the ERA of matter-radiation decoupling Press, W. H. ; Vishniac, E. T. Abstract With particular reference to the pancake theory of galaxy formation, the paper calculates the attenuation or amplification of adiabatic perturbations of a Friedmann cosmology before, during, and after the era of hydrogen recombination and matter-radiation decoupling. The calculation is based on a modified two-fluid (baryon, photon) model which maintains accuracy even when the mean free path of the photon fluid becomes arbitrarily large. It is found that in addition to the damping of radiative viscosity and heat conduction before recombination, damping just during decoupling is important. Consequently there is no 'velocity overshoot' of perturbations to increased amplitude (as had been previously proposed); this probably renders the standard pancake model inconsistent with present limits on the microwave anisotropy. Also, the smallest surviving mass scales ('pancake masses') are quite large, e.g., 2 x 10 to the 16th solar masses, about 120 Mpc, for Omega = 0.1. Publication: The Astrophysical Journal Pub Date: March 1980 DOI: 10.1086/157749 Bibcode: 1980ApJ...236..323P Keywords: Cosmology; Galactic Evolution; Hydrodynamic Equations; Perturbation Theory; Two Fluid Models; Adiabatic Conditions; Conductive Heat Transfer; Differential Equations; Hydrogen Recombinations; Astrophysics full text sources ADS |

A comparison between the quasichemical model and two-fluid local-composition models

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.